Positive solutions of linear elliptic equations with critical growth in the Neumann boundary condition

Miroslav Chlebík, Marek Fila, and Wolfgang Reichel

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Submission date: 07. Feb. 2003 (revised version: April 2003)
Pages: 19
published in: Nonlinear differential equations and applications, 10 (2003) 3, p. 329-346 
DOI number (of the published article): 10.1007/s00030-003-1037-6
Bibtex
MSC-Numbers: 35J65, 35B33
Keywords and phrases: critical sobolev exponent, nonlinear boundary condition
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Abstract:
We study the existence of positive solutions of a linear elliptic equation with critical Sobolev exponent in a nonlinear Neumann boundary condition. We prove a result which is similar to a classical result of Brezis and Nirenberg who considered a corresponding problem with nonlinearity in the equation. Our proof of the fact that the dimension three is critical use a new Pohozaev-type identity.